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 <section id="module-random">
<h1>9.6. <a class="reference internal" href="#module-random" title="random: Generate pseudo-random numbers with various common distributions."><code class="xref py py-mod docutils literal notranslate">random</code></a> — Generate pseudo-random numbers<a class="headerlink" href="#module-random" title="Permalink to this headline">¶</a></h1>
Source code: <a class="reference external" href="https://github.com/python/cpython/tree/2.7/Lib/random.py">Lib/random.py</a>
<hr class="docutils" />
This module implements pseudo-random number generators for various
distributions.
For integers, uniform selection from a range. For sequences, uniform selection
of a random element, a function to generate a random permutation of a list
in-place, and a function for random sampling without replacement.
On the real line, there are functions to compute uniform, normal (Gaussian),
lognormal, negative exponential, gamma, and beta distributions. For generating
distributions of angles, the von Mises distribution is available.
Almost all module functions depend on the basic function <a class="reference internal" href="#random.random" title="random.random"><code class="xref py py-func docutils literal notranslate">random()</code></a>, which
generates a random float uniformly in the semi-open range [0.0, 1.0). Python
uses the Mersenne Twister as the core generator. It produces 53-bit precision
floats and has a period of 2**19937-1. The underlying implementation in C is
both fast and threadsafe. The Mersenne Twister is one of the most extensively
tested random number generators in existence. However, being completely
deterministic, it is not suitable for all purposes, and is completely unsuitable
for cryptographic purposes.
The functions supplied by this module are actually bound methods of a hidden
instance of the <code class="xref py py-class docutils literal notranslate">random.Random</code> class. You can instantiate your own
instances of <code class="xref py py-class docutils literal notranslate">Random</code> to get generators that don’t share state. This is
especially useful for multi-threaded programs, creating a different instance of
<code class="xref py py-class docutils literal notranslate">Random</code> for each thread, and using the <a class="reference internal" href="#random.jumpahead" title="random.jumpahead"><code class="xref py py-meth docutils literal notranslate">jumpahead()</code></a> method to make
it likely that the generated sequences seen by each thread don’t overlap.
Class <code class="xref py py-class docutils literal notranslate">Random</code> can also be subclassed if you want to use a different
basic generator of your own devising: in that case, override the <code class="xref py py-meth docutils literal notranslate">random()</code>,
<code class="xref py py-meth docutils literal notranslate">seed()</code>, <code class="xref py py-meth docutils literal notranslate">getstate()</code>, <code class="xref py py-meth docutils literal notranslate">setstate()</code> and
<code class="xref py py-meth docutils literal notranslate">jumpahead()</code> methods. Optionally, a new generator can supply a
<code class="xref py py-meth docutils literal notranslate">getrandbits()</code> method — this
allows <a class="reference internal" href="#random.randrange" title="random.randrange"><code class="xref py py-meth docutils literal notranslate">randrange()</code></a> to produce selections over an arbitrarily large range.
<div class="versionadded">
New in version 2.4: the <a class="reference internal" href="#random.getrandbits" title="random.getrandbits"><code class="xref py py-meth docutils literal notranslate">getrandbits()</code></a> method.
</div>
As an example of subclassing, the <a class="reference internal" href="#module-random" title="random: Generate pseudo-random numbers with various common distributions."><code class="xref py py-mod docutils literal notranslate">random</code></a> module provides the
<a class="reference internal" href="#random.WichmannHill" title="random.WichmannHill"><code class="xref py py-class docutils literal notranslate">WichmannHill</code></a> class that implements an alternative generator in pure
Python. The class provides a backward compatible way to reproduce results from
earlier versions of Python, which used the Wichmann-Hill algorithm as the core
generator. Note that this Wichmann-Hill generator can no longer be recommended:
its period is too short by contemporary standards, and the sequence generated is
known to fail some stringent randomness tests. See the references below for a
recent variant that repairs these flaws.
<div class="versionchanged">
Changed in version 2.3: MersenneTwister replaced Wichmann-Hill as the default generator.
</div>
The <a class="reference internal" href="#module-random" title="random: Generate pseudo-random numbers with various common distributions."><code class="xref py py-mod docutils literal notranslate">random</code></a> module also provides the <a class="reference internal" href="#random.SystemRandom" title="random.SystemRandom"><code class="xref py py-class docutils literal notranslate">SystemRandom</code></a> class which
uses the system function <a class="reference internal" href="os.html#os.urandom" title="os.urandom"><code class="xref py py-func docutils literal notranslate">os.urandom()</code></a> to generate random numbers
from sources provided by the operating system.
<div class="admonition warning">
Warning
The pseudo-random generators of this module should not be used for
security purposes. Use <a class="reference internal" href="os.html#os.urandom" title="os.urandom"><code class="xref py py-func docutils literal notranslate">os.urandom()</code></a> or <a class="reference internal" href="#random.SystemRandom" title="random.SystemRandom"><code class="xref py py-class docutils literal notranslate">SystemRandom</code></a> if
you require a cryptographically secure pseudo-random number generator.
</div>
Bookkeeping functions:
<dl class="py function">
<dt class="sig sig-object py" id="random.seed">
random.seed(a=None)<a class="headerlink" href="#random.seed" title="Permalink to this definition">¶</a></dt>
<dd>Initialize internal state of the random number generator.
<code class="docutils literal notranslate">None</code> or no argument seeds from current time or from an operating
system specific randomness source if available (see the <a class="reference internal" href="os.html#os.urandom" title="os.urandom"><code class="xref py py-func docutils literal notranslate">os.urandom()</code></a>
function for details on availability).
If a is not <code class="docutils literal notranslate">None</code> or an <a class="reference internal" href="functions.html#int" title="int"><code class="xref py py-class docutils literal notranslate">int</code></a> or a <a class="reference internal" href="functions.html#long" title="long"><code class="xref py py-class docutils literal notranslate">long</code></a>, then
<code class="docutils literal notranslate">hash(a)</code> is used instead. Note that the hash values for some types
are nondeterministic when <a class="reference internal" href="../using/cmdline.html#envvar-PYTHONHASHSEED"><code class="xref std std-envvar docutils literal notranslate">PYTHONHASHSEED</code></a> is enabled.
<div class="versionchanged">
Changed in version 2.4: formerly, operating system resources were not used.
</div>
</dd></dl>

<dl class="py function">
<dt class="sig sig-object py" id="random.getstate">
random.getstate()<a class="headerlink" href="#random.getstate" title="Permalink to this definition">¶</a></dt>
<dd>Return an object capturing the current internal state of the generator. This
object can be passed to <a class="reference internal" href="#random.setstate" title="random.setstate"><code class="xref py py-func docutils literal notranslate">setstate()</code></a> to restore the state.
<div class="versionadded">
New in version 2.1.
</div>
<div class="versionchanged">
Changed in version 2.6: State values produced in Python 2.6 cannot be loaded into earlier versions.
</div>
</dd></dl>

<dl class="py function">
<dt class="sig sig-object py" id="random.setstate">
random.setstate(state)<a class="headerlink" href="#random.setstate" title="Permalink to this definition">¶</a></dt>
<dd>state should have been obtained from a previous call to <a class="reference internal" href="#random.getstate" title="random.getstate"><code class="xref py py-func docutils literal notranslate">getstate()</code></a>, and
<a class="reference internal" href="#random.setstate" title="random.setstate"><code class="xref py py-func docutils literal notranslate">setstate()</code></a> restores the internal state of the generator to what it was at
the time <a class="reference internal" href="#random.getstate" title="random.getstate"><code class="xref py py-func docutils literal notranslate">getstate()</code></a> was called.
<div class="versionadded">
New in version 2.1.
</div>
</dd></dl>

<dl class="py function">
<dt class="sig sig-object py" id="random.jumpahead">
random.jumpahead(n)<a class="headerlink" href="#random.jumpahead" title="Permalink to this definition">¶</a></dt>
<dd>Change the internal state to one different from and likely far away from the
current state. n is a non-negative integer which is used to scramble the
current state vector. This is most useful in multi-threaded programs, in
conjunction with multiple instances of the <code class="xref py py-class docutils literal notranslate">Random</code> class:
<a class="reference internal" href="#random.setstate" title="random.setstate"><code class="xref py py-meth docutils literal notranslate">setstate()</code></a> or <a class="reference internal" href="#random.seed" title="random.seed"><code class="xref py py-meth docutils literal notranslate">seed()</code></a> can be used to force all instances into the
same internal state, and then <a class="reference internal" href="#random.jumpahead" title="random.jumpahead"><code class="xref py py-meth docutils literal notranslate">jumpahead()</code></a> can be used to force the
instances’ states far apart.
<div class="versionadded">
New in version 2.1.
</div>
<div class="versionchanged">
Changed in version 2.3: Instead of jumping to a specific state, n steps ahead, <code class="docutils literal notranslate">jumpahead(n)</code>
jumps to another state likely to be separated by many steps.
</div>
</dd></dl>

<dl class="py function">
<dt class="sig sig-object py" id="random.getrandbits">
random.getrandbits(k)<a class="headerlink" href="#random.getrandbits" title="Permalink to this definition">¶</a></dt>
<dd>Returns a python <a class="reference internal" href="functions.html#long" title="long"><code class="xref py py-class docutils literal notranslate">long</code></a> int with k random bits. This method is supplied
with the MersenneTwister generator and some other generators may also provide it
as an optional part of the API. When available, <a class="reference internal" href="#random.getrandbits" title="random.getrandbits"><code class="xref py py-meth docutils literal notranslate">getrandbits()</code></a> enables
<a class="reference internal" href="#random.randrange" title="random.randrange"><code class="xref py py-meth docutils literal notranslate">randrange()</code></a> to handle arbitrarily large ranges.
<div class="versionadded">
New in version 2.4.
</div>
</dd></dl>

Functions for integers:
<dl class="py function">
<dt class="sig sig-object py" id="random.randrange">
random.randrange(stop)<a class="headerlink" href="#random.randrange" title="Permalink to this definition">¶</a></dt>
<dt class="sig sig-object py">
random.randrange(start, stop[, step])</dt>
<dd>Return a randomly selected element from <code class="docutils literal notranslate">range(start, stop, step)</code>. This is
equivalent to <code class="docutils literal notranslate">choice(range(start, stop, step))</code>, but doesn’t actually build a
range object.
<div class="versionadded">
New in version 1.5.2.
</div>
</dd></dl>

<dl class="py function">
<dt class="sig sig-object py" id="random.randint">
random.randint(a, b)<a class="headerlink" href="#random.randint" title="Permalink to this definition">¶</a></dt>
<dd>Return a random integer N such that <code class="docutils literal notranslate">a &lt;= N &lt;= b</code>.
</dd></dl>

Functions for sequences:
<dl class="py function">
<dt class="sig sig-object py" id="random.choice">
random.choice(seq)<a class="headerlink" href="#random.choice" title="Permalink to this definition">¶</a></dt>
<dd>Return a random element from the non-empty sequence seq. If seq is empty,
raises <code class="xref py py-exc docutils literal notranslate">IndexError</code>.
</dd></dl>

<dl class="py function">
<dt class="sig sig-object py" id="random.shuffle">
random.shuffle(x[, random])<a class="headerlink" href="#random.shuffle" title="Permalink to this definition">¶</a></dt>
<dd>Shuffle the sequence x in place. The optional argument random is a
0-argument function returning a random float in [0.0, 1.0); by default, this is
the function <a class="reference internal" href="#random.random" title="random.random"><code class="xref py py-func docutils literal notranslate">random()</code></a>.
Note that for even rather small <code class="docutils literal notranslate">len(x)</code>, the total number of permutations of
x is larger than the period of most random number generators; this implies
that most permutations of a long sequence can never be generated.
</dd></dl>

<dl class="py function">
<dt class="sig sig-object py" id="random.sample">
random.sample(population, k)<a class="headerlink" href="#random.sample" title="Permalink to this definition">¶</a></dt>
<dd>Return a k length list of unique elements chosen from the population sequence.
Used for random sampling without replacement.
<div class="versionadded">
New in version 2.3.
</div>
Returns a new list containing elements from the population while leaving the
original population unchanged. The resulting list is in selection order so that
all sub-slices will also be valid random samples. This allows raffle winners
(the sample) to be partitioned into grand prize and second place winners (the
subslices).
Members of the population need not be <a class="reference internal" href="../glossary.html#term-hashable">hashable</a> or unique. If the population
contains repeats, then each occurrence is a possible selection in the sample.
To choose a sample from a range of integers, use an <a class="reference internal" href="functions.html#xrange" title="xrange"><code class="xref py py-func docutils literal notranslate">xrange()</code></a> object as an
argument. This is especially fast and space efficient for sampling from a large
population: <code class="docutils literal notranslate">sample(xrange(10000000), 60)</code>.
</dd></dl>

The following functions generate specific real-valued distributions. Function
parameters are named after the corresponding variables in the distribution’s
equation, as used in common mathematical practice; most of these equations can
be found in any statistics text.
<dl class="py function">
<dt class="sig sig-object py" id="random.random">
random.random()<a class="headerlink" href="#random.random" title="Permalink to this definition">¶</a></dt>
<dd>Return the next random floating point number in the range [0.0, 1.0).
</dd></dl>

<dl class="py function">
<dt class="sig sig-object py" id="random.uniform">
random.uniform(a, b)<a class="headerlink" href="#random.uniform" title="Permalink to this definition">¶</a></dt>
<dd>Return a random floating point number N such that <code class="docutils literal notranslate">a &lt;= N &lt;= b</code> for
<code class="docutils literal notranslate">a &lt;= b</code> and <code class="docutils literal notranslate">b &lt;= N &lt;= a</code> for <code class="docutils literal notranslate">b &lt; a</code>.
The end-point value <code class="docutils literal notranslate">b</code> may or may not be included in the range
depending on floating-point rounding in the equation <code class="docutils literal notranslate">a + (b-a) * random()</code>.
</dd></dl>

<dl class="py function">
<dt class="sig sig-object py" id="random.triangular">
random.triangular(low, high, mode)<a class="headerlink" href="#random.triangular" title="Permalink to this definition">¶</a></dt>
<dd>Return a random floating point number N such that <code class="docutils literal notranslate">low &lt;= N &lt;= high</code> and
with the specified mode between those bounds. The low and high bounds
default to zero and one. The mode argument defaults to the midpoint
between the bounds, giving a symmetric distribution.
<div class="versionadded">
New in version 2.6.
</div>
</dd></dl>

<dl class="py function">
<dt class="sig sig-object py" id="random.betavariate">
random.betavariate(alpha, beta)<a class="headerlink" href="#random.betavariate" title="Permalink to this definition">¶</a></dt>
<dd>Beta distribution. Conditions on the parameters are <code class="docutils literal notranslate">alpha &gt; 0</code> and
<code class="docutils literal notranslate">beta &gt; 0</code>. Returned values range between 0 and 1.
</dd></dl>

<dl class="py function">
<dt class="sig sig-object py" id="random.expovariate">
random.expovariate(lambd)<a class="headerlink" href="#random.expovariate" title="Permalink to this definition">¶</a></dt>
<dd>Exponential distribution. lambd is 1.0 divided by the desired
mean. It should be nonzero. (The parameter would be called
“lambda”, but that is a reserved word in Python.) Returned values
range from 0 to positive infinity if lambd is positive, and from
negative infinity to 0 if lambd is negative.
</dd></dl>

<dl class="py function">
<dt class="sig sig-object py" id="random.gammavariate">
random.gammavariate(alpha, beta)<a class="headerlink" href="#random.gammavariate" title="Permalink to this definition">¶</a></dt>
<dd>Gamma distribution. (Not the gamma function!) Conditions on the
parameters are <code class="docutils literal notranslate">alpha &gt; 0</code> and <code class="docutils literal notranslate">beta &gt; 0</code>.
The probability distribution function is:
<div class="highlight-default notranslate"><div class="highlight"><pre> x ** (alpha - 1) * math.exp(-x / beta)
pdf(x) = --------------------------------------
 math.gamma(alpha) * beta ** alpha
</pre></div>
</div>
</dd></dl>

<dl class="py function">
<dt class="sig sig-object py" id="random.gauss">
random.gauss(mu, sigma)<a class="headerlink" href="#random.gauss" title="Permalink to this definition">¶</a></dt>
<dd>Gaussian distribution. mu is the mean, and sigma is the standard
deviation. This is slightly faster than the <a class="reference internal" href="#random.normalvariate" title="random.normalvariate"><code class="xref py py-func docutils literal notranslate">normalvariate()</code></a> function
defined below.
</dd></dl>

<dl class="py function">
<dt class="sig sig-object py" id="random.lognormvariate">
random.lognormvariate(mu, sigma)<a class="headerlink" href="#random.lognormvariate" title="Permalink to this definition">¶</a></dt>
<dd>Log normal distribution. If you take the natural logarithm of this
distribution, you’ll get a normal distribution with mean mu and standard
deviation sigma. mu can have any value, and sigma must be greater than
zero.
</dd></dl>

<dl class="py function">
<dt class="sig sig-object py" id="random.normalvariate">
random.normalvariate(mu, sigma)<a class="headerlink" href="#random.normalvariate" title="Permalink to this definition">¶</a></dt>
<dd>Normal distribution. mu is the mean, and sigma is the standard deviation.
</dd></dl>

<dl class="py function">
<dt class="sig sig-object py" id="random.vonmisesvariate">
random.vonmisesvariate(mu, kappa)<a class="headerlink" href="#random.vonmisesvariate" title="Permalink to this definition">¶</a></dt>
<dd>mu is the mean angle, expressed in radians between 0 and 2*pi, and kappa
is the concentration parameter, which must be greater than or equal to zero. If
kappa is equal to zero, this distribution reduces to a uniform random angle
over the range 0 to 2*pi.
</dd></dl>

<dl class="py function">
<dt class="sig sig-object py" id="random.paretovariate">
random.paretovariate(alpha)<a class="headerlink" href="#random.paretovariate" title="Permalink to this definition">¶</a></dt>
<dd>Pareto distribution. alpha is the shape parameter.
</dd></dl>

<dl class="py function">
<dt class="sig sig-object py" id="random.weibullvariate">
random.weibullvariate(alpha, beta)<a class="headerlink" href="#random.weibullvariate" title="Permalink to this definition">¶</a></dt>
<dd>Weibull distribution. alpha is the scale parameter and beta is the shape
parameter.
</dd></dl>

Alternative Generators:
<dl class="py class">
<dt class="sig sig-object py" id="random.WichmannHill">
class random.WichmannHill([seed])<a class="headerlink" href="#random.WichmannHill" title="Permalink to this definition">¶</a></dt>
<dd>Class that implements the Wichmann-Hill algorithm as the core generator. Has all
of the same methods as <code class="xref py py-class docutils literal notranslate">Random</code> plus the <a class="reference internal" href="#random.whseed" title="random.whseed"><code class="xref py py-meth docutils literal notranslate">whseed()</code></a> method described
below. Because this class is implemented in pure Python, it is not threadsafe
and may require locks between calls. The period of the generator is
6,953,607,871,644 which is small enough to require care that two independent
random sequences do not overlap.
</dd></dl>

<dl class="py function">
<dt class="sig sig-object py" id="random.whseed">
random.whseed([x])<a class="headerlink" href="#random.whseed" title="Permalink to this definition">¶</a></dt>
<dd>This is obsolete, supplied for bit-level compatibility with versions of Python
prior to 2.1. See <a class="reference internal" href="#random.seed" title="random.seed"><code class="xref py py-func docutils literal notranslate">seed()</code></a> for details. <a class="reference internal" href="#random.whseed" title="random.whseed"><code class="xref py py-func docutils literal notranslate">whseed()</code></a> does not guarantee
that distinct integer arguments yield distinct internal states, and can yield no
more than about 2**24 distinct internal states in all.
</dd></dl>

<dl class="py class">
<dt class="sig sig-object py" id="random.SystemRandom">
class random.SystemRandom([seed])<a class="headerlink" href="#random.SystemRandom" title="Permalink to this definition">¶</a></dt>
<dd>Class that uses the <a class="reference internal" href="os.html#os.urandom" title="os.urandom"><code class="xref py py-func docutils literal notranslate">os.urandom()</code></a> function for generating random numbers
from sources provided by the operating system. Not available on all systems.
Does not rely on software state and sequences are not reproducible. Accordingly,
the <a class="reference internal" href="#random.seed" title="random.seed"><code class="xref py py-meth docutils literal notranslate">seed()</code></a> and <a class="reference internal" href="#random.jumpahead" title="random.jumpahead"><code class="xref py py-meth docutils literal notranslate">jumpahead()</code></a> methods have no effect and are ignored.
The <a class="reference internal" href="#random.getstate" title="random.getstate"><code class="xref py py-meth docutils literal notranslate">getstate()</code></a> and <a class="reference internal" href="#random.setstate" title="random.setstate"><code class="xref py py-meth docutils literal notranslate">setstate()</code></a> methods raise
<code class="xref py py-exc docutils literal notranslate">NotImplementedError</code> if called.
<div class="versionadded">
New in version 2.4.
</div>
</dd></dl>

Examples of basic usage:
<div class="highlight-default notranslate"><div class="highlight"><pre>&gt;&gt;&gt; random.random() # Random float x, 0.0 &lt;= x &lt; 1.0
0.37444887175646646
&gt;&gt;&gt; random.uniform(1, 10) # Random float x, 1.0 &lt;= x &lt; 10.0
1.1800146073117523
&gt;&gt;&gt; random.randint(1, 10) # Integer from 1 to 10, endpoints included
7
&gt;&gt;&gt; random.randrange(0, 101, 2) # Even integer from 0 to 100
26
&gt;&gt;&gt; random.choice(&#39;abcdefghij&#39;) # Choose a random element
&#39;c&#39;

&gt;&gt;&gt; items = [1, 2, 3, 4, 5, 6, 7]
&gt;&gt;&gt; random.shuffle(items)
&gt;&gt;&gt; items
[7, 3, 2, 5, 6, 4, 1]

&gt;&gt;&gt; random.sample([1, 2, 3, 4, 5], 3) # Choose 3 elements
[4, 1, 5]
</pre></div>
</div>
<div class="admonition seealso">
See also
M. Matsumoto and T. Nishimura, “Mersenne Twister: A 623-dimensionally
equidistributed uniform pseudorandom number generator”, ACM Transactions on
Modeling and Computer Simulation Vol. 8, No. 1, January pp.3–30 1998.
Wichmann, B. A. &amp; Hill, I. D., “Algorithm AS 183: An efficient and portable
pseudo-random number generator”, Applied Statistics 31 (1982) 188-190.
<a class="reference external" href="http://code.activestate.com/recipes/576707/">Complementary-Multiply-with-Carry recipe</a> for a compatible alternative
random number generator with a long period and comparatively simple update
operations.
</div>
</section>

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